CHE-30043 Materials Chemistry & Catalysis :Solid State Chemistry lecture 3
Rob JacksonLJ1.16, 01782 733042
[email protected]/robjteaching
@robajackson
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Lecture plan
• Compound semiconductors – III/V and II/VI compounds
• Band gaps and the appearance of materials
• Determination of band gaps from conductivity measurements
• Band structures of d block compounds
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Compound semiconductors
• Compound semiconductors are compounds that show semiconductor behaviour (in contrast to the insulating compounds considered earlier).
• A commercially important example is GaAs, gallium arsenide.
• GaAs has a similar structure to Si (the diamond structure) with alternating Ga and As atoms.
http://phycomp.technion.ac.il/~nika/diamond_structure.html
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GaAs
• First, look at the valence electrons:Ga is 4s24p1, As is 4s24p3
• There will be 2 bands formed, each with 4N levels (the band structure will be drawn).
• The lower band will have a greater contribution from As than Ga (nuclear charge higher in As).
• The 8N valence electrons fill the lower band.• The band gap is ~ 1.4 eV.
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Other III/V semiconductors
• GaAs is an example of a III/V semiconductor (a combination of an element from group 3, with one valence electron less than Si, with one from group V, with one valence electron more than Si).
• Other examples are GaSb, InP, InAs and InSb.
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II/VI semiconductors
• II/VI semiconductors are typified by CdTe.• Cd has valence electrons in 5s24d10
• Te has valence electrons in 5s24d105p4
• Band structure is based on 5s and 5p levels from each element.
• The band structure of CdTe will be drawn as an example.
• Other examples include ZnTe and ZnS.
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Compound semiconductors: trend in band gaps
material Band gap 300K, eV material Band gap
300K, eV
GaP 2.25 ZnO* 3.2
GaAs 1.43 ZnS* 3.6
GaSb 0.68 CdSe 1.74
InP 1.27 CdTe 1.44
InAs 0.36 Si 1.11
InSb 0.17 Ge 0.66
Kittel, C., Intro. to Solid State Physics, 6th Ed., New York: John Wiley, 1986, p. 185
* Note wide band gaps
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Applications of semiconductors: photocells – (i)
• A good example of the use of semiconductors is in photocells.
• Photocells work because electricity is conducted and a circuit completed when light shines on a semiconducting material – but thus will only work if the bandgap is in the visible region.
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Applications of semiconductors: photocells – (ii)
• What values of bandgaps are useful?– Use E = hc/– e.g., for a cell to be useful in the visible
region, the bandgap must be low enough for the lowest frequency (longest wavelength) light.
– Red light has =700 nm = 700 x 10-9 m– Calculate E and convert to eV
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Band gaps and colour/appearance of materials - 1
• Absorption/reflection of light by metals and compounds depends on their band structure/band gap, since the photons that are absorbed and then re-emitted will have appropriate frequencies for the band gaps of the materials in question.
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Band gaps and colour/appearance of materials - 2
• Metals – transitions between levels in bands correspond to visible light – shiny appearance.
• Silicon – band gap in lower end of visible region – shiny metallic appearance.
• Insulators (e.g. crystalline NaCl, SiO2) – larger band gaps – higher energy – corresponding, e.g. to UV region – colourless – but changed by defects ...
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Decreasing band gap and colour
Silicon – showing shiny appearance (but not transparent)
C (diamond) – clear and transparent
Germanium – described as ‘grey-white’
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Relationship between band structure and crystal structure in group IV
band gap/eV
C 5.5
Si 1.1
Ge 0.7
Sn 0.1
Pb 0.1
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Crystal structure - 1
• In C, Si and Ge the valence s and p orbitals can combine – hence the sp3 model is a valid description – and all valence electrons go into bonding orbitals and fill the valence band.
• In Sn and Pb there is less overlap of the s and p orbitals so separate bonding and antibonding orbitals are not formed.
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Crystal structure - 2
• Instead the orbitals form a continuous band, with a very small band gap, as in metallic structures.
• In general, the structure that is formed is the one which involves the electrons most in bonding, and this is achieved differently in metals, through having delocalised valence electrons.
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Why the band gap decreases going down the ‘C’ group
• The degree of s, p overlap decreases as nuclear charge increases (going down the group).
• At Sn there is virtually no overlap, and a continuous band is formed from the s and p orbitals.
• As the degree of overlap decreases, both the bond strength, and the difference between bonding and antibonding orbitals decreases.
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Determination of band gaps from conductivity measurements
• An insulator or semiconductor will show an increase in conductance (the inverse of resistance) with temperature.
• Conductance G is related to temperature T by the expression:
G = G0 exp (-Eg / 2kT)
where Eg is the band gap of the material.
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Determination of Eg from data
T/K 300 350 400G 0.1 0.5 3.0
Procedure is to take the expression and take logs of both sides:
ln G = ln G0 – Eg / 2kT
Plot ln G against 1/T, gradient = - Eg / 2kA rough plot will be drawn in the lecture.
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Band structures of d block compounds
• We consider the first row transition metal monoxides:
MO, where M = Ti, V, Mn, Fe, Co and Ni• Structures are based on the rock salt
structure, but their properties differ widely because of the behaviour of the d-orbitals, which control their properties.
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MO Structure revisited
All the MO compounds adopt this structure, but their properties vary widely
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Classification of d-orbitals
• The metal d-orbitals are divided into two sets, one pointing towards the oxide ions and one between them.
• The two sets of orbitals will be drawn, and are also shown on the next slide
(or see Dann pp 111-3)
The t2g orbitals on each metal atom (dxy, dyz, dzx) point towards other metal atoms, and the other d orbitals overlap with orbitals from the oxygen atoms.
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Can bands form?
• If the metal t2g d-orbitals can overlap, then bands can form. Also, these bands will not be fully occupied because the d-orbitals are themselves not filled.
• So, if bands can form, the oxides will have metallic properties and be conductors.
• This applies to TiO and VO.
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Trends in properties along the group
• With TiO and VO there is good overlap of the d orbitals, so they have metallic properties and conduct electricity.
• As we move along the group, the d-orbital electrons become more tightly bound (with increasing nuclear charge) and this inhibits band formation.
• The oxides show semiconductor and then insulator properties.
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TiO VO MnO FeO CoO NiO metals semiconductors insulators
• Colour of the compounds can also be a useful indication of their conductivity. Nickel oxide is green, as is a nickel complex in solution, suggesting discrete nickel ions with well-spaced energy levels.
• Vanadium oxide is black – light is absorbed over the full spectral range, corresponding to many closely spaced energy levels.
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Summary
• Compound semiconductors have been described
• The influence of band gaps on the appearance of materials has been considered
• The determination of band gaps from conductivity measurements has been described
• The band structures of d block compounds has been described